A theory that describes how matter interacts dynamically with the geometry of space and time. It was first published by Einstein in 1915 and is currently used to study the structure and evolution of the universe, as well as having practical applications like GPS.

learn more… | top users | synonyms (1)

2
votes
0answers
44 views

Regular initial data

I have a very basic question. What exactly is meant by "regular" initial data in general relativity? Does it mean smooth? at least $C^{2}$? All literature on the subject just uses this term without ...
1
vote
1answer
268 views

Proper time of circular motion under Schwarzschild metric

I'm trying to calculate the proper time of a massive particle circulating Schwarzschild black hole, using EL equation of the following Lagrangian: ...
2
votes
1answer
135 views

Membrane-reversed black holes and their relationship to white-holes

We usually think of white holes as 'thermodynamically reversed black-holes', and this kind of membranes have not been observed in our universe. However, there is some other kind of 'topologically ...
2
votes
2answers
347 views

Matter and anti-matter collision energy problem

From Beyond Einstein, by Michio Kaku and Jennifer Thompson, Chapter 13, Antimatter : Dirac, also focused on the fact that Einstein's equation $E=mc^2$ wasn't totally true. (Einstein was aware that ...
2
votes
1answer
143 views

From Euler-Lagrange equation to non affine geodesic equation

I have some problems to demonstrate the non affine geodesic equation from Euler-Lagrange's equations. I start defining the Lagrangian $L=\sqrt f$, but then I'm not able to find the Christoffel ...
1
vote
3answers
5k views

Can a light be bent by a magnetic field?

I'm struck with two competing ideas on the question in the title. Listing #1: http://van.physics.illinois.edu/qa/listing.php?id=2009 Q: "How far can a magnetic field bend light?" A: "Unfortunately, ...
2
votes
1answer
177 views

How can I express the Riemann tensor of the 4-metric in terms of quantities derived from the 3-metric and the normal to it?

I want an expression for the Riemann tensor of the four metric in terms of extrinsic curvature, normal, lie derivative of the normal, etc. The first Einstein-Codacci eq. gives the Riemann tensor of ...
4
votes
1answer
92 views

Are there any restrictions on building the topology of spacetime out of the complement of open balls?

I assume that for a Lorentzian manifold (i.e. with Minkowski signature), the analog of an open ball is the interior of a light cone. My question is motivated by the observation that whereas any point ...
5
votes
3answers
1k views

What is the “Event Horizon” of a black hole [duplicate]

Can someone please explain what the event horizon of a black hole is? I mean is it the actual surface of the black hole or is it the point of no return where light can no longer escape?
-2
votes
1answer
466 views

GPS Working Principle [closed]

Hand-held GPS units in modern phones identify your location by (A) transmitting their location and time to GPS satellites. (B) receiving location data of GPS satellites. (C) ...
6
votes
2answers
236 views

What's the basic premise of General Relativity?

What is the basic assumption(s) required to explore general relativity? For example, if one merely assumes that the speed of light $c$ is the same for all observers, and the laws of physics are the ...
1
vote
0answers
44 views

Maximal development/Development of a solution

I'm having troubles to rigorously understand what a development (or maximal development) of a solution is in General Relativity. I was reading a paper by Burnett and Rendall and they write "By maximal ...
1
vote
1answer
267 views

Curvature tensor of 2-sphere using exterior differential forms (tetrads)

$ds^2= r^2 (d\theta^2 + \sin^2{\theta}d\phi^2)$ The following is the tetrad basis $e^{\theta}=r d{\theta} \,\,\,\,\,\,\,\,\,\, e^{\phi}=r \sin{\theta} d{\phi}$ Hence, $de^{\theta}=0 ...
3
votes
1answer
712 views

Problem with calculating the curvature tensor of the $n$ dimensional sphere

I am calculating the Riemann curvature tensor, Ricci curvature tensor, and Ricci scalar of the $n$ sphere $$x_0^2 + x_1^2 + ....+x_n^2=R^2,$$ whose metric is $$ds^2=R^2(d\phi_1^2 + \sin{\phi_1}^2 ...
3
votes
1answer
917 views

Equation for null geodesic around schwarzschild metric?

I'm trying to find the path of a photon around the Schwarzschild black hole, given its initial conditions. After much tribulation, I've basically given up on solving the equations by myself. I just ...
2
votes
2answers
156 views

Entropy difference between initial and final states for a spherical photon cell collapsing in a black hole

Consider a spherical symmetric thin cell of photons converging to a point. At some moment, there is a formation of an horizon and a black hole. But each black hole is evaporating,and so, after some ...
7
votes
2answers
1k views

Time dilation at a black hole [duplicate]

According to the Wikipedia article on black holes: Even though the collapse takes a finite amount of time from the reference frame of infalling matter, a distant observer sees the infalling ...
2
votes
1answer
134 views

Specific energy and specific angular momentum of photon

In this PDF [1], is made reference to specific energy and angular momentum of a particle. If the particle has no mass, like a photon, how should I define these terms in the equations further down for ...
2
votes
0answers
353 views

Trouble with calculating Christoffel symbols of FLRW metric using Lagrangian method

The FLRW metric which I am using is $$ds^2 = dt^2 - \frac{a(t)^2}{c^2} \left( dx^2 + dy^2 + dz^2 \right)$$ where $a(t)$ is the so-called 'scale factor'. I did not want to calculate the Christoffel ...
1
vote
1answer
134 views

Can the vanishing of the Riemann tensor be determined from causal relations?

Given a Lorentzian manifold and metric tensor, "$( M, g )$", the corresponding causal relations between its elements (events) may be derived; i.e. for every pair (in general) of distinct events in set ...
1
vote
2answers
931 views

Kronecker delta confusion

I'm confused about the Kronecker delta. In the context of four-dimensional spacetime, multiplying the metric tensor by its inverse, I've seen (where the upstairs and downstairs indices are the same): ...
7
votes
1answer
1k views

Does potential energy in gravitationall field increase mass?

I was just taught (comments) that any type of energy contributes to mass of the object. This must indeed include potential energy in gravitational field. But here, things cease to make sense, have a ...
1
vote
1answer
104 views

Incompatibility of GR and QM [duplicate]

I am told that the theories of General Relativity and Quantum Mechanics are fundamentally incompatible... Why is that? Someone explained that it had to do with the fact that quantum particles such As ...
2
votes
1answer
223 views

Stringy corrections of Einstein's vacuum field equations

From string theory, the vacuum field equations obtain correction of the order $O[\alpha'R]^n$ such that they can be written as $$ R_{\alpha\beta} -\frac{1}{2}g_{\alpha\beta}R + O[\alpha'R] = 0 $$ ...
-2
votes
1answer
243 views

Gravity as a river [closed]

I understand that gravity is viewed as flowing as a river pushing objects down on the body of a planet. If that is the case and earth is a sphere, where does the gravity go when it hits the center of ...
3
votes
2answers
2k views

Can anyone please explain Hawking-Penrose Singularity Theorems and geodesic incompleteness?

Can anyone please explain Hawking-Penrose Singularity Theorems and geodesic incompleteness? In easy to understand plain English please.
1
vote
2answers
378 views

Solving a light ray worldline with the geodesic equation

I'm having trouble solving the geodesic equation for a light ray. $$ {d^2 x^\mu \over d\tau^2} + \Gamma^\mu_{\alpha\beta} {dx^\alpha \over d\tau} {dx^\beta \over d\tau} = 0 $$ I apologise, but I'm a ...
7
votes
0answers
169 views

What really are exotic supersymmetric black holes?

I have just read (in the black holes chapter 14 on p244 of this book Ref.1) that in string theory, when one adds an (electric?) charge $Q$ to a static black hole, one can arrive at an exotic ...
5
votes
1answer
257 views

Ricci tensor of the orthogonal space

While reading this article I got stuck with Eq.$(54)$. I've been trying to derive it but I can't get their result. I believe my problem is in understanding their hints. They say that they get the ...
7
votes
2answers
381 views

Tensor equations in General Relativity

In the context of general relativity it is often stated that one of the main purposes of tensors is that of making equations frame-independent. Question: why is this true? I'm looking for a ...
10
votes
3answers
1k views

Group Theory in General Relativity

In Special Relativity, the Lorentz Group is the set of matrices that preserve the metric, i.e. $\Lambda \eta \Lambda^T=\eta$. Is there any equivalent in General Relativity, like: $\Lambda g ...
6
votes
2answers
791 views

Einstein Field Equations in other space-time dimensions than 3+1?

This question is apparently quite simple but I can't seem to find an answer to it, so I was hopping anyone could clarify me. Are the Einstein field equations (EFE) only valid for a 3+1 dimensional ...
1
vote
1answer
158 views

How to find distance of closest approach for a Schwarzschild geodesic?

What is the distance of closest approach in this Wikipedia article? I can't seem to find its definition, and this other question doesn't have an answer I can understand.
3
votes
3answers
120 views

Showing Hubble constant is time-independent

I have the following question for homework: Show that the Hubble constant $H$ is time-independent in a universe in which the only contribution to energy density comes from vacuum energy. So in ...
0
votes
1answer
3k views

How does gravity effects both time and light if they have no mass [duplicate]

I've been reading about how black holes can effect both time and light with gravity. So I was wondering, doesn't something have to have mass to be effected by gravity? And if so, does this mean both ...
1
vote
0answers
45 views

Is a dynamical extension of non-commutative black holes feasible?

Non-commutative (sometimes called "fuzzy") black holes are solutions of Einstein's equations obtained with a previous basic assumption of non-commutativity of the coordinates $[x^{\mu},x^{\nu}]=i\, ...
0
votes
1answer
161 views

can be exist the negative mass? [duplicate]

I'm not sure about this but I guess there must be negative masses in the universe because of the symmetry. If the gravity is one of the main forces in nature it must has negatives mass to be able to ...
1
vote
1answer
84 views

Can we build a synthetic event horizon?

If we imagine ourselves to be a civilization capable of manipulating very heavy masses in arbitrary spatial and momentum configurations (because we have access to large amounts of motive force, for ...
2
votes
1answer
163 views

Derivation of Weyl tensor

I want to derive the Weyl tensor along the lines of this derivation, but I am unable to complete it. (I am only interested in $4$ dimension for now.) Every contraction I perform gives either $0=R + 3 ...
4
votes
2answers
172 views

5D Ricci Curvature

As part of a hw problem for a class, we're supposed to be deriving the equivalence given in equation 2.3 of this paper http://arxiv.org/abs/1107.5563. I was wondering if there is some special ...
3
votes
1answer
84 views

Some sort of conservation equation

As far as I know, in General Relativity, an expression of the kind $\nabla_{\mu} X = 0$ states that, associated to $X$, there exist a charge which is conserved. The first example that comes to mind is ...
5
votes
0answers
179 views

Gravitational redshift of Hawking radiation

How can Hawking radiation with a finite (greather than zero) temperature come from the event horizon of a black hole? A redshifted thermal radiation still has Planck spectrum but with the lower ...
1
vote
1answer
135 views

Killing vector argument gone awry?

What has gone wrong with this argument?! The original question A space-time such that $$ds^2=-dt^2+t^2dx^2$$ has Killing vectors $(0,1),(-\exp(x),\frac{\exp(x)}{t}), ...
1
vote
1answer
139 views

Assuming space is infinite can our observable universe be an island amongst an archipelego?

According to recent measurements our observable universe is roughly 93 billion light years in diameter; also it appears (according to WMAP measurements) that spacetime is flat. Supposing space is ...
3
votes
2answers
633 views

Geodesic equations

I am having trouble understanding how the following statement (taken from some old notes) is true: For a 2 dimensional space such that $$ds^2=\frac{1}{u^2}(-du^2+dv^2)$$ the timelike geodesics ...
0
votes
1answer
252 views

Does the actual curvature of spacetime hold energy?

My understanding of GR is that curvature of spacetime reflects the density of energy-matter. Does the curvature itself have energy? Or if energy is assigned to curvature it simply reflects the energy ...
3
votes
2answers
437 views

Excluding big bang itself, does spacetime have a boundary?

My understanding of big bang cosmology and General Relativity is that both matter and spacetime emerged together (I'm not considering time zero where there was a singularity). Does this mean that ...
9
votes
1answer
309 views

Our Universe Can't be Looped? [duplicate]

With reference to the Twin-Paradox (I am new with this), now information of who has actually aged comes from the fact that one of the twins felt some acceleration. So if universe was like a loop, and ...
2
votes
0answers
55 views

How to keep the clock of a spaceship synchronised to the clock of an observer? [duplicate]

I read that the clocks of GPS satellites seem to run slower than the clock of stationary observer, because of their speed (special relativity) and seem to run faster than the clock of stationary ...
3
votes
0answers
144 views

Curvature and spacetime

Suppose that it is given that the Riemann curvature tensor in a special kind of spacetime of dimension $d\geq2$ can be written as $$R_{abcd}=k(x^a)(g_{ac}g_{bd}-g_{ad}g_{bc})$$ where $x^a$ is a ...